A Mass Balance Model that Uses Low-altitude Meteorological Observations and the Area–Altitude Distribution of a Glacier

A glacier mass balance model that requires only low-altitude precipitation and temperature observations and the glacier's areaaltitude distribution is presented as an alternative to direct field measurements. Input to the model for South Cascade Glacier are daily weather observations at stations 30–60 km from the glacier and at altitudes 1300 to 1500 m lower than the glacier. The model relies on the internal consistency of mass balance variables that are generated by simulation using the low-altitude weather data. The daily values of such balance variables as snowline altitude, zero balance altitude, glacier balance, balance flux and the accumulation area ratio are correlated throughout the ablation season using two-degree polynomial regressions to obtain the lowest fitting error. When the minimum average error (or maximum R ²) is attained, the generated balances and other variables are considered to be real. A simplex optimization technique is used to determine the optimal coefficient values that are used in algorithms to convert meteorological observations to snow accumulation and snow and ice ablation. The independently produced simulation results for the 1959–1996 period are compared with balances measured at the glacier. The agreement between annual balances for individual years is fair and between long-term volume changes measured by the geodetic method is excellent.     

Mass Balance Methods on Kongsvegen, Svalbard

On the glacier Kongsvegen (102 km²) in northwest Spitsbergen, Svalbard, traditional mass balance measurements by stake readings and snow surveying have been conducted annually since 1987. In addition, repeated global positioning system (GPS) profiling, shallow core analysis and ground-penetrating radar (GPR) surveying have been applied. The purpose of this paper is to evaluate the input from the different methods, especially the GPS profiling, using the results from the traditional direct method as a reference. The annual flow rate on Kongsvegen is low (2 ? 3 m a^?1), and the emergence velocity is almost negligible. Thus the geometry changes of the glacier, i.e. the change in altitude per distance from the head of the glacier, should reflect the change in net balance of the glacier. The mean annual altitude change from the longitudinal, centreline GPS profiles was compared to the direct stake readings and showed a very good agreement. On Kongsvegen the measured actual ice flux is so low that the mass transfer down-glacier at the mean equlibrium line altitude is less than 10% of what is needed to maintain steady-state geometry. This is clearly shown in the changing altitude profiles. GPS profiling can be used on large glaciers in remote areas to monitor geometry changes, ice flow and net mass balance changes. However, it requires that the centreline profile changes are representative for the area/altitude intervals, i.e. that the accumulation and ablation pattern is evenly distributed. For this purpose the GPR surveying quickly gave the snow distribution variability over long distances. Shallow cores drilled in different altitudes in the accumulation area were analysed to detect radioactive reference layers from the fallout after the Chernobyl accident in 1986, and showed very good agreement to the direct measured net balance. Thus older reference horizons from bomb tests in 1962 could be used to extend the net balance series backwards.     

Reconstruction and Regional Significance of the Coire Breac Palaeoglacier,Glen Esk,Eastern Grampian Highlands,Scotland

We present a glaciological and climatic reconstruction of a former glacier in Coire Breac, an isolated cirque within the Eastern Grampian plateau of Scotland, 5 km from the Highland edge. Published glacier reconstructions of presumed Younger Dryas‐age glaciers in this area show that equilibrium line altitudes decreased steeply towards the east coast, implying a arctic maritime glacial environment. Extrapolation of the ELA trend surface implies that glaciers should have existed in suitable locations on the plateau, a landscape little modified by glaciation. In Coire Breac, a 0.35 km² cirque glacier existed with an equilibrium line altitude of 487 ± 15 m above present sea level. The equilibrium line altitude matches closely the extrapolated regional equilibrium line altitude trend surface for Younger Dryas Stadial glaciers. The mean glacier thickness of 24 m gives an ice volume of 7.8 × 10⁶ m³, and a maximum basal shear stress of c. 100 kPa^?1. Ablation gradient was c. –0.0055 m m^?1, with a mean July temperature at the equilibrium line altitude of c. 5.1°C. The reconstruction implies an arctic maritime climate of low precipitation with local accumulation enhanced by blown snow, which may explain the absence of other contemporary glaciers nearby. Reconstructed ice flow lines show zones of flow concentration around the lower ice margin which help to explain the distribution of depositional facies associated with a former debris cover which may have delayed eventual glacier retreat. No moraines in the area have been dated, so palaeoclimatic interpretations remain provisional, and a pre‐Lateglacial Interstadial age cannot be ruled out.     

Measurements and Models of the Mass Balance of Hintereisferner

This paper summarizes the methods applied to determine the mass balance of Hintereisferner and several other glaciers in the Tyrolean Alps since 1952. On an annual basis the direct glaciological method was applied with fixed date measurements on 10–15 accumulation pits and 30–90 ablation stakes on 9 km².
Indirect mass balance determination from equilibrium line altitude, accumulation area ratios or representative stakes, yield fair results and some exceptions could be related to anomalous meteorological conditions.
Monthly or more frequent stake readings supplied time series of ablation at various altitudes and slope aspects that served as basis for the calibration of energy and mass balance models. Of various models developed, two are presented in this paper. Both are based on degree days, one using daily values from a valley station to predict the mean annual balance of the entire glacier, while the other calculates day-to-day changes at 50-m grid points on the glacier.
The geodetic method has been applied for longer periods and yields results consistent with those of the glaciological method. The balance velocity calculated from recent ice thickness soundings and accumulation measurements is significantly less than observed velocity.     

EVALUATION OF GRIDDED PRECIPITATION FOR NORWAY USING GLACIER MASS‐BALANCE MEASUREMENTS

The service seNorge ( http://senorge.no ) provides gridded temperature and precipitation for mainland Norway. The products are provided as interpolated station measurements on a 1 × 1 km grid. Precipitation gauges are predominantly located at lower elevations such as coastal areas and valleys. Therefore, there are large uncertainties in extrapolating precipitation data to higher altitudes, both due to sparsity of observations as well as the large spatial variability of precipitation in mountainous regions. Using gridded temperature and precipitation data from seNorge, surface mass balance was modeled for five Norwegian glaciers of different size and climate conditions. The model accounts for melting of snow and ice by applying a degree‐day approach and considers refreezing assuming a snow depth depended storage. Calculated values are compared to point measurements of glacier winter mass balance. On average for each glacier, modeled and measured surface mass‐balance evolutions agree well, but results at individual stake locations show large variability. Two types of problems were identified: first, grid data were not able to capture spatial mass balance variability at smaller glaciers. Second, a significant increase in the bias between model and observations with altitude for one glacier suggested that orographic enhancement of precipitation was not appropriately captured by the gridded interpolation.     

The thermal structure of Hansbreen, a tidewater glacier in southern Spitsbergen, Svalbard

Ice temperature measurements were taken from three shallow and five deep (to bedrock) boreholes on Hansbreen, Svalbard, in selected years between 1988 and 1994. In general, results show a subpolar, polythermal structure. The glacier accumulation zone is of warm ice within the entire vertical profile except the uppermost layer of seasonal temperature fluctuations where there is an upper cold ice layer in the ablation zone which varies in thickness and may even be absent in the western lateral part. The upper layer of cold ice thins along the glacier centre-line from the equilibrium line altitude down to the glacier front. The depth of the pressure melting, indicating the base of the cold ice layer, was defined at the borehole measurement sites but was not manifested as an internal reflection horizon using multi-frequency radar methods. The isotherm lies about 20 m above a radar internal reflecting horizon near the equilibrium line altitude and about 40 m above it in the frontal part of the glacier. The internal reflection horizon almost certainly reflects the high water content within temperate ice and not the cold/temperate ice interface. At 10 m depth, the temperatures are 2–3°C higher than the calculated mean annual air temperatures, demonstrating the importance of meltwater refreezing on the release of latent heat.     

RESPONSE OF A MONTENEGRO GLACIER TO EXTREME SUMMER HEATWAVES IN 2003 AND 2007

The Debeli Namet glacier in the Durmitor massif, Montenegro, is one of the lowest altitude glaciers (2050–2300 m) at this latitude (42–44°N) in the northern hemisphere. The glacier survives well below the climatological equilibrium line altitude because of substantial inputs from avalanching and windblown snow. The glacier survived two of the hottest summers on record in 2003 and 2007, although it experienced significant retreat. However, during the intervening years (2004–2006) the glacier increased in size and advanced, forming a new frontal moraine. This rapid advance was primarily in response to much cooler summer temperatures, close to or cooler than average, and a marked increase in winter precipitation. The rapid growth and decay of the Debeli Namet glacier in response to inter‐annual climate variability highlights the sensitivity of small cirque glaciers to short‐term climate change.     

The Impact Of Extreme Summer Melt on Net Accumulation of an Avalanche Fed Glacier,as Determined by Ground‐Penetrating Radar

Glacier mass balance is more sensitive to warming than cooling, but feedbacks related to the exposure of previously buried firn and ice in very warm years is not generally considered in sensitivity studies. A ground‐penetrating radar survey in the accumulation area of Rolleston Glacier, New Zealand shows that five years of previous net accumulation was removed by melt from parts of the glacier above the long‐term equilibrium line altitude during a single negative mass balance year. Rolleston Glacier receives a large amount of accumulation from snow avalanches, which may temporarily buffer it from climate warming by providing additional mass that has accumulated at higher elevations, effectively increasing the elevation range of the glacier. However, glaciers reliant on avalanche input may have high sensitivity to climatic variations because the extra mass is concentrated on a small part of the glacier, and small variations in avalanche input could have a large impact on overall glacier accumulation. Further research is needed to better estimate the amount and spatial distribution of accumulation by avalanche in order to quantify the climate sensitivity of small avalanche‐fed glaciers.     

An analysis of short-term albedo variations at Haut Glacier d'Arolla, Switzerland

Abstract An analysis of ten‐minute albedo variations, recorded on Haut Glacier d'Arolla, Switzerland, over an 11 day period in the 1999 ablation season is presented. Most of the short‐term (<1 day) albedo variability is caused by variations in cloud cover, while solar zenith angle variations in the range 25° to 75° are of minor importance, probably due to the predominantly cloudy conditions during the measurement period. A new method to calculate albedo variation as a function of cloud cover is developed. Short‐term albedo variations are expressed by the ratio of the measured albedo to the daily albedo ‘minimum’, defined as the albedo under cloud‐free conditions when the solar zenith angle is <50°. Variations in cloud cover are quantified by the ratio of the measured incoming shortwave radiation flux to the theoretical direct‐beam shortwave radiation flux. The resulting relationships are successful, explaining 83% and 87–90% of short‐term albedo variation on snow and ice respectively, and may be incorporated into albedo parameterizations already used in numerical energy balance melt models, without the need for additional data. Simulations with a glacier energy balance model suggest that melt rates are overestimated by between 1 and 3 mm water equivalent per day if a correction is not made for the increase in albedo under cloudy conditions. Other causes of albedo variation are identified and evidence is found for the removal of fine debris from the glacier surface by intense rainfall, leading to an albedo increase. The implications for energy balance models and satellite‐derived albedo measurements are discussed.     

Measurement and Estimative Models of Glacier Mass Balance in China

Attributed to high altitude and inland location, the glaciers in China are characterized by very low temperature. The non-negligible contribution of up to 25% of superimposed ice to the net balance has been taken into account in the mass budget calculation. So too has the internal the accumulation in the infiltration zone of the accumulation area.
The prevailing monsoon climate delivers most of the annual precipitation over glaciated areas of China in the summer, making the major accumulation on those glaciers coincide with the ablation period. Therefore, the annual mass balance should be calculated neither by giving the place of annual accumulation to winter balance, nor annual ablation to summer balance. Rather, it is better done by net accumulation and net ablation during the year. In order to get the annual accumulation and the annual ablation on a glacier, the summer precipitation should be measured at the same time.
Frequent snowfall in the summer season results in intensive fluctuation of surface albedo. This means that, for lack of data on the extremes of ablation, reconstruction of mass balance is unsatisfactory when based on the relationships of accumulation and ablation to precipitation and temperature. The establishment of models, either on the relationship of multi-year mass balance to the equilibrium line and the mass balance gradient of a glacier in steady-state, or on the maximum entropy principle and the hydrometeorological data, helps to estimate the multi-year mass balance of the glacierized area in a mountain range or drainage basin.     

Surface Heat Balance and Spatially Distributed Ablation Modelling at Koryto Glacier, Kamchatka Peninsula, Russia

To investigate the characteristics of ablation at Koryto Glacier, a mountain glacier under maritime climate in Kamchatka Peninsula, Russia, we made field observations from August to early September 2000. At a site near the equilibrium line, the 31‐day average net radiation, sensible heat flux, and latent heat flux were 43, 59 and 31 W^?2, respectively. We developed a new distributed ablation model, which only needs measurements of air temperature and global radiation at one site. Hourly ablation rates at this site obtained by the energy balance method are related to measured air temperature and global radiation by linear multiple regression. A different set of multiple regression coefficients is fitted for snow and ice surfaces. Better estimates of ablation rate can be obtained by this approach than by other temperature index models. These equations are then applied to each grid cell of a digital elevation model to estimate spatially distributed hourly melt. Air temperature is extrapolated using a constant temperature lapse rate and global radiation is distributed considering topographic effects. The model enables us to calculate the hourly spatial distribution of ablation rates within the glacier area and could well provide a realistic simulation of ablation over the whole glacier.     

Snow and sea ice thermodynamics in the Arctic:Model validation and sensitivity study against SHEBA data

Evolution of the Arctic sea ice and its snow cover during the SHEBA year were simulated by applying a high-resolution thermodynamic snow/ice model (HIGHTSI).Attention was paid to the impact of albedo on snow and sea ice mass balance,effect of snow on total ice mass balance,and the model vertical resolution. The SHEBA annual simulation was made applying the best possible external forcing data set created by the Sea Ice Model Intercomparison Project.The HIGHTSI control run reasonably reproduced the observed snow and ice thickness.A number of albedo schemes were incorporated into HIGHTSI to study the feedback processes between the albedo and snow and ice thickness.The snow thickness turned out to be an essential variable in the albedo parameterization.Albedo schemes dependent on the surface temperature were liable to excessive positive feedback effects generated by errors in the modelled surface temperature.The superimposed ice formation should be taken into account for the annual Arctic sea ice mass balance.     

Collins Glacier Retreat Process and Regional Climatic Variations,King George Island,Antarctica

This paper investigates the recent climatic variability and changes in snow line and ice front position in Collins Glacier, King George Island, South Shetland Islands, Antarctic Peninsula. This region has recorded one of the largest temperature increases in the past fifty years and has been demonstrated to be highly sensitive to climate changes. To monitor recent changes (1983–2006), we determined the fluctuations of the terminus and snow line of the glacier via remote sensing data and field observation in the summer of 2013. We conclude that the Collins Glacier has responded slowly to regional climate changes (decades or even centuries), as glacial responses to climatic events do not depend solely on one environmental variable. The glacier presented more retreat and elevation of the snow line in the north sector. The retreat data are correlated with the mean monthly temperature and annual number of days of melting‐degree variations.     

Decadal‐Scale Changes of the Ödenwinkelkees,Central Austria,Suggest Increasing Control of Topography and Evolution Towards Steady State

Small mountain glaciers have short mass balance response times to climate change and are consequently very important for short‐term contributions to sea level. However, a distinct research and knowledge gap exists between (1) wider regional studies that produce overview patterns and trends in glacier changes, and (2) in situ local scale studies that emphasise spatial heterogeneity and complexity in glacier responses to climate. This study of a small glacier in central Austria presents a spatiotemporally detailed analysis of changes in glacier geometry and changes in glaciological behaviour. It integrates geomorphological surveys, historical maps, aerial photographs, airborne LiDAR data, ground‐based differential global positioning surveys and Ground Penetrating Radar surveys to produce three‐dimensional glacier geometry at 13 time increments spanning from 1850 to 2013. Glacier length, area and volume parameters all generally showed reductions with time. The glacier equilibrium line altitude increased by 90 m between 1850 and 2008. Calculations of the mean bed shear stress rapidly approaching less than 100 kPA, of the volume–area ratio fast approaching 1.458, and comparison of the geometric reconstructions with a 1D theoretical model could together be interpreted to suggest evolution of the glacier geometry towards steady state. If the present linear trend in declining ice volume continues, then the Ödenwinkelkees will disappear by the year 2040, but we conceptualise that non‐linear effects of bed overdeepenings on ice dynamics, of supraglacial debris cover on the surface energy balance, and of local topographically driven controls, namely wind‐redistributed snow deposition, avalanching and solar shading, will become proportionally more important factors in the glacier net balance.     

Spatiotemporal index for analyzing controls on snow climatology: application in the Colorado Front Range

Mountain snowpacks are important water supplies that are susceptible to climate change, yet snow measurements are sparse relative to snowpack heterogeneity. We used remote sensing to derive a spatiotemporal index of snow climatology that reveals patterns in snow accumulation, persistence, and ablation. Then we examined how this index relates to climate, terrain, and vegetation. Analyses were based on Moderate Resolution Imaging Spectroradiometer eight-day snow cover from 2000 to 2010 for a mountain watershed in the Colorado Front Range, USA. The Snow Cover Index (SCI) was calculated as the fraction of years that were snow covered for each pixel. The proportion of SCI variability explained by independent variables was evaluated using regression analysis. Independent variables included elevation, northing, easting, slope, aspect, northness, solar radiation, precipitation, temperature, and vegetation cover. Elevation was the dominant control on SCI patterns, due to its influence on both temperature and precipitation. Grouping SCI values by elevation, we identified three distinct snow zones in the basin: persistent, transitional, and intermittent. The transitional snow zone represents an area that is sensitive to losing winter snowpack. The SCI can be applied to other basins or regions to identify dominant controls on snow cover patterns and areas sensitive to snow loss.     

南极乔治王岛柯林斯冰帽冰川发育条件

柯林斯冰帽具有显著的海洋性气候特征。据笔者实测资料 ,该冰帽冬季和夏季温度垂直递减率相当 ,为 0 .6 5℃ 1 0 0m ,冰区与无冰区间的温跃值约为 0 .3℃。年、日较差小 ,夏季气温较低 ,平衡线上夏季 (1 2月— 2月 )的平均温度为 0℃。同时 ,云雾多 ,湿度大 ,冰面接受到的太阳辐射小 ,形成了有利于冰川发育的热量条件。同时频繁的极地气旋活动给冰帽区带来了以固态降水为主的较丰沛的降水 ,成为有利于冰川发育的物质条件。夏季温度较低和年降水较丰沛是该冰帽发育有利的水热条件。     

南极乔治王岛柯林斯冰帽小冰穹物质平衡特征的初步分析

柯林斯冰帽小冰穹属于冷季补给型冰川。该冰穹高差不大，但末端比顶部的消融期长两个月；暖季消融随高度上升迅速递减。冷季积累随高度的变化显著。ＳＤＳ断面１９９１／１９９２年度物质平衡差额为１６３ｍｍ，零平衡线海拔高度为１４０ｍ，比动力平衡线低２０ｍ。其物质平衡特征表现为物质平衡梯度较大，而物质平衡水平较低，稳定性系数较小，反映了亚极地海洋性气候下冰川物质平衡的特有性质     

Inferring Glacier Mass Balance Using Radarsat: Results From Peyto Glacier, Canada

The capability of RADARSAT synthetic aperture radar (SAR) for the purpose of snow-line/accumulation area mapping for a temperate alpine glacier is examined. In agreement with other orbital C-band SAR studies, RADARSAT can discriminate between firn and bare ice facies. Limited observations are reported with respect to the electromagnetic variability of the ice facies in the ablation area, but they are inconclusive. Operational considerations are discussed with respect to reconciling the uncertainties of late-summer weather and their possible impact on the dielectric and scattering properties of the glacier surface. Vagaries associated with other glacier settings, mass balance states and their associated facies configurations are discussed including the difficulty of using the transient snow-line to define the equilibrium line and the lower extent of the accumulation area for glaciers where superimposed ice may form.
The radar remote-sensing reconnaissance of equilibrium line altitude (ELA) and accumulation area ratio (AAR) for estimating glacier mass balance requires serious consideration in those instances where traditional ground measurements used in the direct glaciological method are absent. However, with respect to the ELA, such estimates can vary depending on the accuracy of the reference digital elevation information. Moreover, for many glacier configurations, where mass balance variations due to altitude are influenced or in some cases completely masked by local balance variations, defining the ELA may be an irreconcilable problem. Using the AAR may be more robust in this regard. It is further determined that the total error inherent in the reconnaissance method would have serious implications for the confident estimation of mass balance normals and climate-related trends if the method were to be utilized over the longer term.     

Current Behaviour and Dynamics of the Lowermost Italian Glacier (Montasio Occidentale,Julian Alps)

Smaller glaciers (<0.5 km²) react quickly to environmental changes and typically show a large scatter in their individual response. Accounting for these ice bodies is essential for assessing regional glacier change, given their high number and contribution to the total loss of glacier area in mountain regions. However, studying small glaciers using traditional techniques may be difficult or not feasible, and assessing their current activity and dynamics may be problematic. In this paper, we present an integrated approach for characterizing the current behaviour of a small, avalanche‐fed glacier at low altitude in the Italian Alps, combining geomorphological, geophysical and high‐resolution geodetic surveying with a terrestrial laser scanner. The glacier is still active and shows a detectable mass transfer from the accumulation area to the lower ablation area, which is covered by a thick debris mantle. The glacier owes its existence to the local topo‐climatic conditions, ensured by high rock walls which enhance accumulation by delivering avalanche snow and reduce ablation by providing topographic shading and regulating the debris budget of the glacier catchment. In the last several years the glacier has displayed peculiar behaviour compared with most glaciers of the European Alps, being close to equilibrium conditions in spite of warm ablation seasons. Proportionally small relative changes have also occurred since the Little Ice Age maximum. Compared with the majority of other Alpine glaciers, we infer for this glacier a lower sensitivity to air temperature and a higher sensitivity to precipitation, associated with important feedback from increasing debris cover during unfavourable periods.     

西南极洲纳尔逊冰帽的表面运动

本文通过对纳尔逊冰帽冰面速度和应变率的分析,得出冰帽边缘的最大夏季表面速度为2058m/a,最大年平均表面速度为15.5m/a,探求了冰面运动速度的空间分布和季节性变化,冰帽顶部的表面应变率为+0.0079/a和+0.0034/a。还讨论了冰面应变率从冰帽顶点到边缘的变化特点及其与冰面裂隙的关系。并将这些特征同我国大陆型冰帽进行了对比,从冰川动力学的角度阐明了纳尔逊冰帽的某些特征。